3x^2+10x-135=0

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Solution for 3x^2+10x-135=0 equation: 


Simplifying
3x2 + 10x + -135 = 0

Reorder the terms:
-135 + 10x + 3x2 = 0

Solving
-135 + 10x + 3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-45 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 3.333333333x + 45 + x2 = 0 + 45

Reorder the terms:
-45 + 45 + 3.333333333x + x2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 3.333333333x + x2 = 0 + 45
3.333333333x + x2 = 0 + 45

Combine like terms: 0 + 45 = 45
3.333333333x + x2 = 45

The x term is 3.333333333x.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333x + 2.777777779 + x2 = 45 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = 45 + 2.777777779

Combine like terms: 45 + 2.777777779 = 47.777777779
2.777777779 + 3.333333333x + x2 = 47.777777779

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 47.777777779

Calculate the square root of the right side: 6.912147118

Break this problem into two subproblems by setting 
(x + 1.666666667) equal to 6.912147118 and -6.912147118.


Subproblem 1
x + 1.666666667 = 6.912147118

Simplifying
x + 1.666666667 = 6.912147118

Reorder the terms:
1.666666667 + x = 6.912147118

Solving
1.666666667 + x = 6.912147118

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = 6.912147118 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = 6.912147118 + -1.666666667
x = 6.912147118 + -1.666666667

Combine like terms: 6.912147118 + -1.666666667 = 5.245480451
x = 5.245480451

Simplifying
x = 5.245480451


Subproblem 2
x + 1.666666667 = -6.912147118

Simplifying
x + 1.666666667 = -6.912147118

Reorder the terms:
1.666666667 + x = -6.912147118

Solving
1.666666667 + x = -6.912147118

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = -6.912147118 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = -6.912147118 + -1.666666667
x = -6.912147118 + -1.666666667

Combine like terms: -6.912147118 + -1.666666667 = -8.578813785
x = -8.578813785

Simplifying
x = -8.578813785


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.245480451, -8.578813785}

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